Plane maps with denominator. Part III: Nonsimple focal points and related bifurcations

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 2, 2005, Pages 451-496

  Bischi, Gian Italo ^a   Gardini, Laura ^a   Mira, Christian ^a  

^a UNIVERSITY OF URBINO   (Italy)

Author keywords

Bifurcations; Focal points; Noninvertible maps; Prefocal sets; Vanishing denominator

Indexed keywords

CHAOS THEORY; CHARACTERIZATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PROBLEM SOLVING; SET THEORY;

FOCAL POINTS; NONINVERTIBLE MAPS; PREFOCAL SETS; VANISHING DENOMINATORS;

BIFURCATION (MATHEMATICS);

EID: 18644375707     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405012314     Document Type: Article

References (21)

1. Abraham, R., Gardini, L. & Mira, C. [1997] Chaos in Discrete Dynamical Systems (A Visual Introduction in Two Dimensions) (Springer-Verlag, NY).
2. Billings, L. & Curry, J. H. [1996] ''On noninvertible maps of the plane: Eruptions," Chaos 6, 108-119.
3. Billings, L., Curry, J. H. & Phipps, E. [1997] "Lyapunov exponents, singularities, and a riddling bifurcation." Phys. Rev. Lett. 79, 1018-1021.
4. Bischi, G. I. & Gardini, L. [1997]' "Basin fractalization due to focal points in a class of triangular maps," Int. J. Bifurcation and Chaos 7, 1555-1577.
5. Bischi, G. I. & Naimzada, A. [1997] "Global analysis of a nonlinear model with learning," Economic Notes 26, 143-174.
6. Bischi, G. I. & Gardini, L. [1999] "Focal points and basin fractalization in some rational maps," in Grazer Mathematische Berichte 339, 61-84.
7. Bischi, G. I., Gardini, L. & Mira, C. [1999] "Maps with denominator. Part I: Some generic properties," Int. J. Bifurcation and Chaos 9, 119-153.
8. Bischi, G. I., Mira, C. & Gardini, L. [2000] "Unbounded sets of attraction," Int. J. Bifurcation and Chaos 10, 1437-1469.
9. Bischi, G. I., Gardini, L. & Mira, C. [2001a] "Maps with a vanishing denominator. A survey of some results," Nonlin. Anal. Th. Meth. Appl. 47, 2171-2185.
10. Bischi, G. I., Kopel, M. & Naimzada, A. [2001b] ''On a rent-seeking game described by a non-invertible iterated map with denominator." Nonlin. Anal. Th. Meth. Appl. 47, 5309-5324.
11. Bischi, G. I., Gardini, L. & Mira, C. [2003] "Plane maps with denominator. Part II: Noninvertible maps with simple focal points," Int. J. Bifurcation and Chaos 13, 2253-2277.
12. Brock, W. A. & Hommes, C. H. [1997] "A rational route to randomness," Econometrica 65, 1059-1095.
13. Foroni, I., Gardini, L. & Barkley Rosser Jr., J. [2003] "Adaptive and statistical expectations in a renewable resource market," Math. Comput. Simul. 63, 541-567.
14. Gardini, L., Bischi, G. I., Fournier-Prunaret, D. [1999] "Basin boundaries and focal points in a map coming from Bairstow's methods," Chaos 9, 367-380.
15. Gumowski, I. & Mira, C. [1980] Dynamique Chaotique. Transition ordre-désordre (Cepadues Editions, Toulouse).
16. Mira, C. [1987] Chaotic Dynamics. From, the One-Dimensional Endomorphism to the Two-Dimensional Diffeomorphism (World Scientific, Singapore).
17. Mira, C., Fournier-Prunaret, D., Gardini, L., Kawakami, H. & Cathala, J. C. [1994] "Basin bifurcations of two-dimensional noninvertible maps: Fractalization of basins," Int. J. Bifurcation and Chaos 4, 343-381.
18. Mira, C., Gardini, L., Barugola, A. & Cathala, J. C. [1996a] Chaotic Dynamics in Two-Dimensional Non-invertible Maps (World Scientific, Singapore).
19. Mira, C., Millerioux, G., Carcasses, J. P. & Gardini, L. [1996b] "Plane foliation of two-dimensional non-invertible maps," Int. J. Bifurcation and Chaos 6. 1439-1462.
20. 2) maps not defined in the whole plane," Grazer Mathematische Berichte (special issue Proc. ECIT96) 339, 261-278.
21. Yee, H. C. & Sweby, P. K. [1994] "Global asymptotic behavior of iterative implicit schemes," Int. J. Bifurcation and Chaos 4, 1579-1611.